The present invention relates to non-contact measurement of the shape of an object, and, more particularly, to an optical method and device for measuring the shape of an object by triangulation.
Triangulation has long been used to measure surface profiles. Representative patents in the field include those of Korth (U.S. Pat. No. 3,866,038), Lowrey, Jr. et al. (U.S. Pat. No. 3,986,774), Pryor et al. (U.S. Pat. No. 4,373,804), Rioux (U.S. Pat. Nos. 4,627,734, 4,645,347 and 5,177,556) and Yoshimura et al. (U.S. Pat. No. 5,111,056). Triangulation devices, for example the device of Lowrey et al., commonly are used for quality control in manufacturing, to verify that the workpieces being manufactured have the correct shapes.
FIG. 1 shows schematically a typical triangulation device. A light source 10 shines an incident beam 20 of light on a workpiece whose distance along beam 20 from light source 10 is to be determined. FIG. 1A shows two workpieces, 30 and 32, at two different distances from light source 10. Preferably, a means is provided for ensuring that beam 20 illuminates only a small part of workpiece 30 or 32. This can be done by providing an optical system (not shown) for collimating beam 20, or for focusing beam 20 on workpiece 30 or 32. The incident light is reflected diffusely in all directions from a small spot 22 on workpiece 30, or from a small spot 24 on workpiece 32. Some of that reflected light is intercepted by an optical system 50 that is represented in FIG. 1 as two lenses 52 and 54. Optical system 50 focuses the intercepted light on a sensor 60 that is responsive to the position at which the intercepted light is focused thereupon. Typically, sensor 60 is a one dimensional array of charge coupled detectors. Optical system 50 is characterized by a theoretical focal point 56: all the light entering optical system 50 from a point along beam 20 strikes a point on array 60 determined by tracing a straight ray from the point along beam 20 through focal point 56. In FIG. 1, a ray 42 extends from spot 22 via focal point 56 to a point 62 on array 60, and a ray 44 extends from spot 24 via focal point 56 to a point 64 on array 60. Thus, all of the light diffusely reflected from spot 22 that is intercepted by optical system 50 strikes sensor 60 at or near point 62, and all of the light diffusely reflected from spot 24 that is intercepted by optical system 50 strikes sensor 60 at or near point 64. It follows that the distance of a workpiece from light source 10 is a linear function of the position along sensor 60 at which light diffusely reflected from the workpiece is focused by optical system 50.
Spots 22 and 24 are not point light sources. Therefore their focused images on sensor 60 are not geometric points. Typically, the images of spots focused on sensor 60 are spread over several pixels of sensor 60, and the point on sensor 60 used to infer the distance to the workpiece is the center of gravity of the measured intensity.
Triangulation by this method suffers from several deficiencies. One is that the numerical aperture of optical system 50 is small relative to the amount of light reflected from the workpiece, so most of the reflected light is wasted. Another is that the measurement becomes increasingly difficult and imprecise as the surface of the workpiece departs from perpendicularity to incident beam 20. If the surface is nearly parallel to incident beam 20, the intensity of the light reflected diffusely towards optical system 50 is very low relative to the intensity reflected in the specular direction. Furthermore, the focused image on sensor 60 is spread out further, by an amount proportional to the secant of the angle between incident beam 20 and the surface. This degrades the accuracy of the measurement. If the surface is truly parallel to incident beam 20, as is the case for interior walls 35 and 36 of workpiece 34 of FIG. 2A, or if the surface is reentrant, as is the case for workpiece 38 of FIG. 2B, the distance to the surface cannot be measured at all.
A third deficiency relates to the surface roughness of the workpiece. If the tilt of the surface relative to incident beam 20 varies substantially within the spot created by incident beam 20 on the surface, then the intensity of the light reflected diffusely towards optical system 50 is not uniform across the spot, so the center of gravity of the measured intensity is displaced from where it would be if the intensity were uniform, leading to an erroneous distance estimate. Similarly, if the reflectivity profile of the surface is not Lambertian, then the center of gravity of the measured intensity is displaced in a way that leads to a systematic error in the distance estimate. This is illustrated in FIG. 3 for workpiece 30: a Lambertian reflectivity profile 26 produces an image having a symmetrical intensity profile 66 on sensor 60, whereas a non-Lambertian reflectivity profile 28 produces an image having an asymmetric intensity profile 68 on sensor 60. FIG. 3 shows workpiece 30 perpendicular to incident beam 20; the problem illustrated is even more severe for surfaces that are tilted with respect to incident beam 20.
There is thus a widely recognized need for, and it would be highly advantageous to have, a triangulation method that overcomes the deficiencies listed above of the prior art methods.